Properties

Label 3520.2.by
Level $3520$
Weight $2$
Character orbit 3520.by
Rep. character $\chi_{3520}(791,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $0$
Newform subspaces $0$
Sturm bound $1152$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.by (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 352 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 0 \)
Sturm bound: \(1152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

Total New Old
Modular forms 2336 0 2336
Cusp forms 2272 0 2272
Eisenstein series 64 0 64

Decomposition of \(S_{2}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)